The Full Surplus Extraction Theorem with Hidden Actions

I consider a situation in which a principal commits to a mechanism first and then agents choose unobservable actions before they draw their types. The agents’ actions affect not only their payoffs directly but also a distribution of private types as well. Thus, the distribution of types is determined endogenously rather than exogeneously unlike standard mechanism design literature. Then I extend Cremer and McLean’s full surplus extraction theorem [10] to such a setting, that is, identify a necessary and sufficient condition on the information structure for the full surplus extration. More importantly, it implies that the full surplus extraction may not be obtained for generic set of information structure in this more general setting. This contrasts with the standard full surplus extraction theorem which holds generically. I show, however, that the principal can extract all the surplus for any completely mixed action profile for almost all information structure by using more general mechanisms in which agents announce both their types and the realizations of their mixed actions. Since any pure action profile can be arbitrarily approximated by a completely mixed action profile, the principal can virtually extracts all the maximized social surplus. JEL classification: C72, D44, D82